I know this was a previous thread, but I just stumbled across a lengthy test done by golfcity.com with the flagstick in and out. See picture... this was 3 different lines at 3 different speed, both with the stick in and out. 100 drops/putts total. Results were interesting.
My 2 cents..... I think if I’m putting downhill, I’m not pulling the stick. Any other time it will depend on how aggressive a putt I’m going for... soft or hard roll, along with how fast the greens are playing. Def changes things!